In what direction should the aircraft head?

[razored]

Homework Statement

The pilot of an aircraft wishes to fly due west in a 50.0 km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 205 km/h.
a.In what direction should the aircraft head?
b. What should its speed be relative to the ground?

Homework Equations

c^2 = a^2 + b^2

The Attempt at a Solution

for the degree, i got 13.7 but the answer is 14.1 north of west
tan^-1 = (50/205) = 13.7
for the speed, I did (-50) ^2 + (-205)^2 = c^2, but that didn't match the answer of 1.99km/h

 

[dx]

whats your reasoning?

 

[razored]

Well, i put it into a triangle, -50km/h going south, -205km/h west, then found the hypotenuse, which does not match the answer. For the angle, I realize that the angle given in the answer is north west, while mine was south of west, I just don't know where to begin.

 

[dx]

why did you put 205 going west? isn't that the direction you want to find? try 205 at some unknows angle, say $$\theta$$, and then find what $$\theta$$ should be if you want the final direction to be west.

 

[dx]

heres a picture that may help you.

 

[razored]

Wouldn't the 205 be on the X axis because it is without the wind. The speed with the wind would be the hypotenuse I assumed.

 

[dx]

205 km/h is the speed of the plane without wind. not its velocity. now if you add wind, its speed will change, and also its direction, whatever direction it was in. if it was flying directly into the wind, its direction would be the same, i.e opposite to the wind, and its speed would be reduced. you have to choose the direction of the plane with speed 205 km/h such that the direction is changed such that it moves west.

 

[HallsofIvy]

You want the "resultant"- the sum of the wind and the airplanes motion- that is to be "due West"- along the x-axis. It is the 205 km/h that is the hypotenuse of the triangle.